Peterson Nurseries just paid a $3.20 annual dividend. The company has a policy whereby the dividend increases by 3% annually. You would like to purchase 100 shares of stock in this ﬁrm but
Realize that you will not have the funds to do so for another two years. If you desire a 12% rate of
Return, how much should you expect to pay for 100 shares when you can afford to buy this stock?

Question

Quizplus · Accepted Answer

First, we need to calculate the expected dividend for the next two years:
Annual dividend after one year = $3.20 x 1.03 = $3.296
Annual dividend after two years = $3.296 x 1.03 = $3.389
Next, we need to calculate the present value of the expected dividends:
PV = (Div1 / (1+r)^1) + (Div2 / (1+r)^2)
PV = ($3.296 / 1.12^1) + ($3.389 / 1.12^2)
PV = $2.939 + $2.730
PV = $5.669
Finally, we need to add the present value of the expected dividends to the present value of the price of the stock in two years:
PV = $5.669 + (P / 1.12^2)
Where P is the price of the stock in two years. Solving for P, we get:
P = $3.885
Therefore, you should expect to pay $3,885 for 100 shares of this stock when you can afford to buy it.

Peterson Nurseries Just Paid a $3